Estimating Default Correlations Using Simulated Asset Values

Osei Antwi; Dadzie Joseph; Louis Appiah Gyekye

doi:doi:10.11648/j.sjams.20150301.13

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Estimating Default Correlations Using Simulated Asset Values

Osei Antwi, Dadzie Joseph, Louis Appiah Gyekye

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 1)

Received: 7 January 2015 Accepted: 21 January 2015 Published: 2 February 2015

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Abstract

We outline the ingredients necessary to compute the Joint Default Probability from which we obtain Default Correlation, an important risk quantity in the determination of Internal Rating Based Approach in Basel II and III documents on banking supervision and regulations. We discuss Merton’s structural approach of which one key drawback is the difficulty in tracking and calibrating asset value processes and the limitations of variant models which tend to be analytically too complex and compu¬tationally intensive. We address these issues by simulating all the possible asset value processes of a firm whose asset paths we assume to be Gaussian. By generating random values that simulate all the possible asset value processes, we are able to capture all the possible default horizons within a certain macroeconomic framework. Drawing standardised normally distributed assets values of obligors we obtain a range of values of Joint Default Probabilities at a specified asset correlation from which the corresponding range of default correlations are obtained. The results is a simplified approach to the determination of default correlation, easily implementable in Excel and less analytically complicated than existing procedures.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 1)
DOI	10.11648/j.sjams.20150301.13
Page(s)	14-21
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Obligor, Probability of Default, Joint Default Probability, Asset Correlation, Default Threshold, Default Correlation

References

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[2]	Black, F. and Scholes, M., “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, Vol. 81, pp.637-654, 1973.
[3]	Merton R C, On the pricing of corporate debt: the risk structure of interest Rates, Journal of Finance, Vol. 29, pp. 449-70, 1974.
[4]	Jarrow, R. and Turnbull, S., “Credit Risk: Drawing the Analogy,” Risk Magazine, Vol. 5, No.9, 1992.
[5]	Jarrow, R. and Turnbull, S. “Pricing Derivatives on Financial Securities Subject to Credit Risk, Journal of Finance, Vol. 50, No.1, pp. 53-85, 1995.
[6]	Duffie, D. and Singleton, K, “Modeling Term Structures of Defaultable Bonds, Review of Financial Studies, Vol. 12, No.4, pp. 197-226, 1999.
[7]	Bielecki, T. and Rutkowski, M. Credit Risk: Modeling, Valuation and Hedging. New York, Springer-Verlag, 2002.
[8]	Rogers, L. C. G., “Modelling Credit Risk.” Working Paper, University of Bath, 1999.
[9]	Lando, D., Credit Risk Modeling: Theory and Applications, Princeton University Press, NJ, 2003.
[10]	Jarrow, R., vanDeventer, D., andWang, X. “A Robust Test of Merton’s Structural Model for Credit Risk Journal of Risk, Vol.6, No.1, pp. 39–58, 2003.
[11]	Suresh Sundaresan, A Review of Merton’s Model of the Firm’s Capital Structure with its Wide Applications Finance & Economics Division, Columbia Business School, Columbia University, The Annual Review of Financial Economics, Vol. 5, pp. 5.1–5.21. 2013.
[12]	Robert A. Jarrow, and Philip Protter, Structural Versus Reduced Form Models: A New Information Based Perspective, Journal of Investment Management, Vol. 2, No. 2, 2004.
[13]	Navneet Arora, J.R. Bohn, and F. Zhu. Reduced Form vs. Structural Models of credit risk: A Case Study of three Models, Journal of Investment Management, Vol. 3 No. 4 pp. 43, 2005.
[14]	Douglas J. Lucas, Default Correlation and Credit Analysis, the Journal of Fixed Income, Vol. 4, No. 4, pp. 76-87, 1995.
[15]	Stefan Huschens, Konstantin Vogl, Robert Wania, Estimation of Default Probabilities and Default Correlations, pp. 239-258, 2005.
[16]	Krishan Nagpal and Reza Bahar, Measuring default correlation, Risk magazine, Vol. 14, No. 3, pp. 129–132, March 2001.
[17]	G. Loffler, P. N. Posch, Credit Risk Modeling using Excel and VBA, John Wiley & Sons, Chichester, England, 2007.
[18]	Morten Virenfeldt, Deriving Obligor Default Correlations Using Factor Modelling, www.tools4risk.com, July 27, 2010.
[19]	Equation Editor, Microsoft word 2010

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APA Style

Osei Antwi, Dadzie Joseph, Louis Appiah Gyekye. (2015). Estimating Default Correlations Using Simulated Asset Values. Science Journal of Applied Mathematics and Statistics, 3(1), 14-21. https://doi.org/10.11648/j.sjams.20150301.13

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ACS Style

Osei Antwi; Dadzie Joseph; Louis Appiah Gyekye. Estimating Default Correlations Using Simulated Asset Values. Sci. J. Appl. Math. Stat. 2015, 3(1), 14-21. doi: 10.11648/j.sjams.20150301.13

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AMA Style

Osei Antwi, Dadzie Joseph, Louis Appiah Gyekye. Estimating Default Correlations Using Simulated Asset Values. Sci J Appl Math Stat. 2015;3(1):14-21. doi: 10.11648/j.sjams.20150301.13

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@article{10.11648/j.sjams.20150301.13,
  author = {Osei Antwi and Dadzie Joseph and Louis Appiah Gyekye},
  title = {Estimating Default Correlations Using Simulated Asset Values},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {1},
  pages = {14-21},
  doi = {10.11648/j.sjams.20150301.13},
  url = {https://doi.org/10.11648/j.sjams.20150301.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150301.13},
  abstract = {We outline the ingredients necessary to compute the Joint Default Probability from which we obtain Default Correlation, an important risk quantity in the determination of Internal Rating Based Approach in Basel II and III documents on banking supervision and regulations. We discuss Merton’s structural approach of which one key drawback is the difficulty in tracking and calibrating asset value processes and the limitations of variant models which tend to be analytically too complex and compu¬tationally intensive. We address these issues by simulating all the possible asset value processes of a firm whose asset paths we assume to be Gaussian. By generating random values that simulate all the possible asset value processes, we are able to capture all the possible default horizons within a certain macroeconomic framework. Drawing standardised normally distributed assets values of obligors we obtain a range of values of Joint Default Probabilities at a specified asset correlation from which the corresponding range of default correlations are obtained. The results is a simplified approach to the determination of default correlation, easily implementable in Excel and less analytically complicated than existing procedures.},
 year = {2015}
}

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TY  - JOUR
T1  - Estimating Default Correlations Using Simulated Asset Values
AU  - Osei Antwi
AU  - Dadzie Joseph
AU  - Louis Appiah Gyekye
Y1  - 2015/02/02
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150301.13
DO  - 10.11648/j.sjams.20150301.13
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 14
EP  - 21
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150301.13
AB  - We outline the ingredients necessary to compute the Joint Default Probability from which we obtain Default Correlation, an important risk quantity in the determination of Internal Rating Based Approach in Basel II and III documents on banking supervision and regulations. We discuss Merton’s structural approach of which one key drawback is the difficulty in tracking and calibrating asset value processes and the limitations of variant models which tend to be analytically too complex and compu¬tationally intensive. We address these issues by simulating all the possible asset value processes of a firm whose asset paths we assume to be Gaussian. By generating random values that simulate all the possible asset value processes, we are able to capture all the possible default horizons within a certain macroeconomic framework. Drawing standardised normally distributed assets values of obligors we obtain a range of values of Joint Default Probabilities at a specified asset correlation from which the corresponding range of default correlations are obtained. The results is a simplified approach to the determination of default correlation, easily implementable in Excel and less analytically complicated than existing procedures.
VL  - 3
IS  - 1
ER  -

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Author Information

Osei Antwi

Mathematics and Statistics Department, Accra Polytechnic, Accra, Ghana
Dadzie Joseph

Mathematics and Statistics Department, Accra Polytechnic, Accra, Ghana
Louis Appiah Gyekye

Research & Innovations Center, Accra Polytechnic, Accra, Ghana

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Plain Text BibTeX RIS

APA Style

Osei Antwi, Dadzie Joseph, Louis Appiah Gyekye. (2015). Estimating Default Correlations Using Simulated Asset Values. Science Journal of Applied Mathematics and Statistics, 3(1), 14-21. https://doi.org/10.11648/j.sjams.20150301.13

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ACS Style

Osei Antwi; Dadzie Joseph; Louis Appiah Gyekye. Estimating Default Correlations Using Simulated Asset Values. Sci. J. Appl. Math. Stat. 2015, 3(1), 14-21. doi: 10.11648/j.sjams.20150301.13

Copy | Download

AMA Style

Osei Antwi, Dadzie Joseph, Louis Appiah Gyekye. Estimating Default Correlations Using Simulated Asset Values. Sci J Appl Math Stat. 2015;3(1):14-21. doi: 10.11648/j.sjams.20150301.13

Copy | Download

@article{10.11648/j.sjams.20150301.13,
  author = {Osei Antwi and Dadzie Joseph and Louis Appiah Gyekye},
  title = {Estimating Default Correlations Using Simulated Asset Values},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {1},
  pages = {14-21},
  doi = {10.11648/j.sjams.20150301.13},
  url = {https://doi.org/10.11648/j.sjams.20150301.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150301.13},
  abstract = {We outline the ingredients necessary to compute the Joint Default Probability from which we obtain Default Correlation, an important risk quantity in the determination of Internal Rating Based Approach in Basel II and III documents on banking supervision and regulations. We discuss Merton’s structural approach of which one key drawback is the difficulty in tracking and calibrating asset value processes and the limitations of variant models which tend to be analytically too complex and compu¬tationally intensive. We address these issues by simulating all the possible asset value processes of a firm whose asset paths we assume to be Gaussian. By generating random values that simulate all the possible asset value processes, we are able to capture all the possible default horizons within a certain macroeconomic framework. Drawing standardised normally distributed assets values of obligors we obtain a range of values of Joint Default Probabilities at a specified asset correlation from which the corresponding range of default correlations are obtained. The results is a simplified approach to the determination of default correlation, easily implementable in Excel and less analytically complicated than existing procedures.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Estimating Default Correlations Using Simulated Asset Values
AU  - Osei Antwi
AU  - Dadzie Joseph
AU  - Louis Appiah Gyekye
Y1  - 2015/02/02
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150301.13
DO  - 10.11648/j.sjams.20150301.13
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 14
EP  - 21
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150301.13
AB  - We outline the ingredients necessary to compute the Joint Default Probability from which we obtain Default Correlation, an important risk quantity in the determination of Internal Rating Based Approach in Basel II and III documents on banking supervision and regulations. We discuss Merton’s structural approach of which one key drawback is the difficulty in tracking and calibrating asset value processes and the limitations of variant models which tend to be analytically too complex and compu¬tationally intensive. We address these issues by simulating all the possible asset value processes of a firm whose asset paths we assume to be Gaussian. By generating random values that simulate all the possible asset value processes, we are able to capture all the possible default horizons within a certain macroeconomic framework. Drawing standardised normally distributed assets values of obligors we obtain a range of values of Joint Default Probabilities at a specified asset correlation from which the corresponding range of default correlations are obtained. The results is a simplified approach to the determination of default correlation, easily implementable in Excel and less analytically complicated than existing procedures.
VL  - 3
IS  - 1
ER  -

Copy | Download